Question: Solve for $x$ and $y$ using elimination. ${-2x+4y = -8}$ ${3x-5y = 14}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $3$ and the bottom equation by $2$ ${-6x+12y = -24}$ $6x-10y = 28$ Add the top and bottom equations together. $2y = 4$ $\dfrac{2y}{{2}} = \dfrac{4}{{2}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-2x+4y = -8}\thinspace$ to find $x$ ${-2x + 4}{(2)}{= -8}$ $-2x+8 = -8$ $-2x+8{-8} = -8{-8}$ $-2x = -16$ $\dfrac{-2x}{{-2}} = \dfrac{-16}{{-2}}$ ${x = 8}$ You can also plug ${y = 2}$ into $\thinspace {3x-5y = 14}\thinspace$ and get the same answer for $x$ : ${3x - 5}{(2)}{= 14}$ ${x = 8}$